Elements of descriptive geometry ; with their application to spherical trigonometry, spherical projections, and warped surfaces /

Mode of access: Internet.

Elements of geometry: containing the first six books of Euclid, with a supplement on the quadrature of the circle, and the geometry of solids: to which are added, elements of plane and spherical trigonometry,

Mode of access: Internet.

Geometry, plane, solid, and spherical, in six books. To which is added, in an appendix, the theory of projection.

Mode of access: Internet.

Plane and solid geometry. To which is added plane and spherical trigonometry and mensuration.

Mode of access: Internet.

Elements of descriptive geometry; with applications to spherical, perspective and isometric projections, and to shades and shadows,

Mode of access: Internet.

Dynamical Casimir effect for a massless scalar field between two concentric spherical shells

In this work we consider the dynamical Casimir effect for a massless scalar field-under Dirichlet boundary conditions-between two concentric spherical shells. We obtain a general expression for the average number of particle creation, for an arbitrary law of radial motion of the spherical shells, using two distinct methods: by computing the density operator of the system and by calculating the Bogoliubov coefficients. We apply our general expression to breathing modes: when only one of the shells oscillates and when both shells oscillate in or out of phase. Since our results were obtained in the framework of the perturbation theory, under resonant breathing modes they are restricted to a short-time approximation. We also analyze the number of particle production and compare it with the results for the case of plane geometry.

Dynamic Analysis Model of Spherical Roller Bearings with Defects

Rolling element bearings are essential components of rotating machinery. The spherical roller bearing (SRB) is one variant seeing increasing use, because it is self-aligning and can support high loads. It is becoming increasingly important to understand how the SRB responds dynamically under a variety of conditions. This doctoral dissertation introduces a computationally efficient, three-degree-of-freedom, SRB model that was developed to predict the transient dynamic behaviors of a rotor-SRB system. In the model, bearing forces and deflections were calculated as a function of contact deformation and bearing geometry parameters according to nonlinear Hertzian contact theory. The results reveal how some of the more important parameters; such as diametral clearance, the number of rollers, and osculation number; influence ultimate bearing performance. Distributed defects, such as the waviness of the inner and outer ring, and localized defects, such as inner and outer ring defects, are taken into consideration in the proposed model. Simulation results were verified with results obtained by applying the formula for the spherical roller bearing radial deflection and the commercial bearing analysis software. Following model verification, a numerical simulation was carried out successfully for a full rotor-bearing system to demonstrate the application of this newly developed SRB model in a typical real world analysis. Accuracy of the model was verified by comparing measured to predicted behaviors for equivalent systems.

Coolability of porous core debris beds : Effects of bed geometry and multi-dimensional flooding

This thesis addresses the coolability of porous debris beds in the context of severe accident management of nuclear power reactors. In a hypothetical severe accident at a Nordic-type boiling water reactor, the lower drywell of the containment is flooded, for the purpose of cooling the core melt discharged from the reactor pressure vessel in a water pool. The melt is fragmented and solidified in the pool, ultimately forming a porous debris bed that generates decay heat. The properties of the bed determine the limiting value for the heat flux that can be removed from the debris to the surrounding water without the risk of re-melting. The coolability of porous debris beds has been investigated experimentally by measuring the dryout power in electrically heated test beds that have different geometries. The geometries represent the debris bed shapes that may form in an accident scenario. The focus is especially on heap-like, realistic geometries which facilitate the multi-dimensional infiltration (flooding) of coolant into the bed. Spherical and irregular particles have been used to simulate the debris. The experiments have been modeled using 2D and 3D simulation codes applicable to fluid flow and heat transfer in porous media. Based on the experimental and simulation results, an interpretation of the dryout behavior in complex debris bed geometries is presented, and the validity of the codes and models for dryout predictions is evaluated. According to the experimental and simulation results, the coolability of the debris bed depends on both the flooding mode and the height of the bed. In the experiments, it was found that multi-dimensional flooding increases the dryout heat flux and coolability in a heap-shaped debris bed by 47–58% compared to the dryout heat flux of a classical, top-flooded bed of the same height. However, heap-like beds are higher than flat, top-flooded beds, which results in the formation of larger steam flux at the top of the bed. This counteracts the effect of the multi-dimensional flooding. Based on the measured dryout heat fluxes, the maximum height of a heap-like bed can only be about 1.5 times the height of a top-flooded, cylindrical bed in order to preserve the direct benefit from the multi-dimensional flooding. In addition, studies were conducted to evaluate the hydrodynamically representative effective particle diameter, which is applied in simulation models to describe debris beds that consist of irregular particles with considerable size variation. The results suggest that the effective diameter is small, closest to the mean diameter based on the number or length of particles.

Fractal geometry of aggregate snowflakes revealed by triple wavelength radar measurements

Radar reflectivity measurements from three different wavelengths are used to retrieve information about the shape of aggregate snowflakes in deep stratiform ice clouds. Dual-wavelength ratios are calculated for different shape models and compared to observations at 3, 35 and 94 GHz. It is demonstrated that many scattering models, including spherical and spheroidal models, do not adequately describe the aggregate snowflakes that are observed. The observations are consistent with fractal aggregate geometries generated by a physically-based aggregation model. It is demonstrated that the fractal dimension of large aggregates can be inferred directly from the radar data. Fractal dimensions close to 2 are retrieved, consistent with previous theoretical models and in-situ observations.

The surface geometry of exotic nuclei

We analyze the surface geometry of the spherical even-even Ca, Ni, Sn and Pb nuclei using two approaches: The relativistic Dirac-Hartree-Bogoliubov one with several parameter sets and the non-relativistic Hartree-Fock-Bogoliubov one with the Gogny force. The proton and neutron density distributions are fitted to two-parameter Fermi density distributions to obtain the half-density radii and diffuseness parameters. Those parameters allow us to determine the nature of the neutron skins predicted by the models. The calculations are compared with existing experimental data. © 2007 American Institute of Physics.

Characterization of granite matrix porosity and pore-space geometry by in situ and laboratory methods

Most available studies of interconnected matrix porosity of crystalline rocks are based on laboratory investigations; that is, work on samples that have undergone stress relaxation and were affected by drilling and sample preparation. The extrapolation of the results to in situ conditions is therefore associated with considerable uncertainty, and this was the motivation to conduct the ‘in situ Connected Porosity’ experiment at the Grimsel Test Site (Central Swiss Alps). An acrylic resin doped with fluorescent agents was used to impregnate the microporous granitic matrix in situ around an injection borehole, and samples were obtained by overcoring. The 3-D structure of the porespace, represented by microcracks, was studied by U-stage fluorescence microscopy. Petrophysical methods, including the determination of porosity, permeability and P -wave velocity, were also applied. Investigations were conducted both on samples that were impregnated in situ and on non-impregnated samples, so that natural features could be distinguished from artefacts. The investigated deformed granites display complex microcrack populations representing a polyphase deformation at varying conditions. The crack population is dominated by open cleavage cracks in mica and grain boundary cracks. The porosity of non-impregnated samples lies slightly above 1 per cent, which is 2–2.5 times higher than the in situ porosity obtained for impregnated samples. Measurements of seismic velocities (Vp ) on spherical rock samples as a function of confining pressure, spatial direction and water saturation for both non-impregnated and impregnated samples provide further constraints on the distinction between natural and induced crack types. The main conclusions are that (1) an interconnected network of microcracks exists in the whole granitic matrix, irrespective of the distance to ductile and brittle shear zones, and (2) conventional laboratory methods overestimate the matrix porosity. Calculations of contaminant transport through fractured media often rely on matrix diffusion as a retardation mechanism.

Reduction of truncation errors in planar, cylindrical and partial spherical near-field antenna measurements

A method to reduce truncation errors in near-field antenna measurements is presented. The method is based on the Gerchberg-Papoulis iterative algorithm used to extrapolate band-limited functions and it is able to extend the valid region of the calculated far-field pattern up to the whole forward hemisphere. The extension of the valid region is achieved by the iterative application of a transformation between two different domains. After each transformation, a filtering process that is based on known information at each domain is applied. The first domain is the spectral domain in which the plane wave spectrum (PWS) is reliable only within a known region. The second domain is the field distribution over the antenna under test (AUT) plane in which the desired field is assumed to be concentrated on the antenna aperture. The method can be applied to any scanning geometry, but in this paper, only the planar, cylindrical, and partial spherical near-field measurements are considered. Several simulation and measurement examples are presented to verify the effectiveness of the method.

Greenland and Antarctic ice sheet topography, cavity geometry, and global bathymetry (RTopo-2), links to NetCDF files

The ocean plays an important role in modulating the mass balance of the polar ice sheets by interacting with the ice shelves in Antarctica and with the marine-terminating outlet glaciers in Greenland. Given that the flux of warm water onto the continental shelf and into the sub-ice cavities is steered by complex bathymetry, a detailed topography data set is an essential ingredient for models that address ice-ocean interaction. We followed the spirit of the global RTopo-1 data set and compiled consistent maps of global ocean bathymetry, upper and lower ice surface topographies and global surface height on a spherical grid with now 30-arc seconds resolution. We used the General Bathymetric Chart of the Oceans (GEBCO, 2014) as the backbone and added the International Bathymetric Chart of the Arctic Ocean version 3 (IBCAOv3) and the Interna- tional Bathymetric Chart of the Southern Ocean (IBCSO) version 1. While RTopo-1 primarily aimed at a good and consistent representation of the Antarctic ice sheet, ice shelves and sub-ice cavities, RTopo-2 now also contains ice topographies of the Greenland ice sheet and outlet glaciers. In particular, we aimed at a good representation of the fjord and shelf bathymetry sur- rounding the Greenland continent. We corrected data from earlier gridded products in the areas of Petermann Glacier, Hagen Bræ and Sermilik Fjord assuming that sub-ice and fjord bathymetries roughly follow plausible Last Glacial Maximum ice flow patterns. For the continental shelf off northeast Greenland and the floating ice tongue of Nioghalvfjerdsfjorden Glacier at about 79°N, we incorporated a high-resolution digital bathymetry model considering original multibeam survey data for the region. Radar data for surface topographies of the floating ice tongues of Nioghalvfjerdsfjorden Glacier and Zachariæ Isstrøm have been obtained from the data centers of Technical University of Denmark (DTU), Operation Icebridge (NASA/NSF) and Alfred Wegener Institute (AWI). For the Antarctic ice sheet/ice shelves, RTopo-2 largely relies on the Bedmap-2 product but applies corrections for the geometry of Getz, Abbot and Fimbul ice shelf cavities.

Two geometrical memoirs on the general properties of cones of the second degree, and on the spherical conics /

Mode of access: Internet.

The influence of tool geometry on the performance of drilling tools

The main objective of the work presented in this thesis is to investigate the two sides of the flute, the face and the heel of a twist drill. The flute face was designed to yield straight diametral lips which could be extended to eliminate the chisel edge, and consequently a single cutting edge will be obtained. Since drill rigidity and space for chip conveyance have to be a compromise a theoretical expression is deduced which enables optimum chip disposal capacity to be described in terms of drill parameters. This expression is used to describe the flute heel side. Another main objective is to study the effect on drill performance of changing the conventional drill flute. Drills were manufactured according to the new flute design. Tests were run in order to compare the performance of a conventional flute drill and non conventional design put forward. The results showed that 50% reduction in thrust force and approximately 18% reduction in torque were attained for the new design. The flank wear was measured at the outer corner and found to be less for the new design drill than for the conventional one in the majority of cases. Hole quality, roundness, size and roughness were also considered as a further aspect of drill performance. Improvement in hole quality is shown to arise under certain cutting conditions. Accordingly it might be possible to use a hole which is produced in one pass of the new drill which previously would have required a drilled and reamed hole. A subsidiary objective is to design the form milling cutter that should be employed for milling the foregoing special flute from drill blank allowing for the interference effect. A mathematical analysis in conjunction with computing technique and computers is used. To control the grinding parameter, a prototype drill grinder was designed and built upon the framework of an existing cincinnati cutter grinder. The design and build of the new grinder is based on a computer aided drill point geometry analysis. In addition to the conical grinding concept, the new grinder is also used to produce spherical point utilizing a computer aided drill point geometry analysis.